Unaware, as session's incomplete? Have second thoughts (8)

I believe the answer is:

reassess

I'm a little stuck... Click here to teach me more about this clue!

'unaware as session's incomplete? have second thoughts' is the definition.
I can't tell whether this defines the answer.

'unaware as session's incomplete? have' is the wordplay.
'have' indicates the answer is hidden within the clue.
'REASSESS' is hidden within 'unaware as sessions incomplete'.

Can you help me to learn more?

(Other definitions for reassess that I've seen before include "Have second thoughts" , "Examine again" , "Make another appraisal" , "size up again" , "judge again" .)

I've seen this clue in The Everyman puzzle in The Observer.

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